A gas mixture consists of 8 moles of argon and 6 moles of oxygen at temperature $$T$$. Neglecting all vibrational modes, the total internal energy of the system is

8 mol Ar (monoatomic): $$U_1=8\cdot\frac{3}{2}RT=12RT$$.

6 mol O₂ (diatomic, no vibration): $$U_2=6\cdot\frac{5}{2}RT=15RT$$.

Total: $$U=12RT+15RT=27RT$$.

The answer is Option (3): $$27RT$$.

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